The air in an automobile tire with a volume of 0.53 ft3 is at 90oF and 20 psig. Determine the mass of air that must be added to raise the pressure to the recommended value of 30 psig. Assume atmospheric pressure is 14.7 psia and both the temperature and the volume of the air in the tire remain constant as it is inflated. Assume that the air in the tire behaves as an ideal gas, but then check the validity of this assumption.
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I am attempting to prove that the assumption of air as an ideal gas is correct, but I get reduced pressure values of 13.7, Tr=2.3, and when I try to see if molar volume is greater than 20L/mol, I get 6 L/mol. Is the assumption wrong? Or am I?
Anonymous 11:57 AM:
The problem is given in American Engineering units and your question uses SI units. Did you convert everything to SI ? That is taking the hard approach to this problem AND kind of avoiding learning to deal with American Engineering units.
I don't know the critical temperature and pressure of air offhand, so it is not easy for me to check your values of Tr and Pr, but the molar volume of 6 L/mole is not correct. Did you by any chance use MW, Tr and Pr of water here ? Just a guess.
For the 2 states in this problem, I got about 8 and 28 L/mole (but I did the problem in AmEngr units).
The key here is that if we boldly consider air to be a DIATOMIC gas (N2 and O2), then these molar volumes are large enough for us to consider air to be an ideal gas to TWO significant digits. In fact, your answer of 6 would make the air an IG because 6 L/mol > 5 L/mol.
I hope this is helpful!
How does one convert from a gauge pressure to an absolute pressure?
I found the answer to my own question.... Gauge pressure is the pressure difference above atmospheric pressure.
Dave:
Yep, exactly. Good work.
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